CSC 213 – Large Scale Programming

Trees  Represent hierarchical relationships  Parent-child basis of this abstract data type  Real-world example: directories & types csc213/ homeworks/ ideas.todo 1M programs/ LLQueue.java 10K DLNode.java 25K hard.txt 3K impossible.txt 2K Tree.java 20K

Trees  Represent hierarchical relationships  Parent-child basis of this abstract data type  Real-world example: organization classification Mammal Cat Ape LionHumanChimpanzee ProfessorsYankees Fan

Tree Terms  Defined by relationships  Talk about parents, siblings, descendant  Tree rooted at node A  “Top” or “Start” of tree  B, C, D are children of A  A is parent of B, C, D  B, C, D are siblings A BDC G H E F I J K

Tree Relationships  Nodes either leaf or interior  Both or neither not options  A, B, C, F are parents  At least 1 child for each  Also called “interior nodes”  "Leaves" name of others  Leaf node has no children A BDC G H E F I J K

Trees Recursion  Trees are recursive structure  Subtree defined by a node  C is root of this subtree  E root of this subtree  Trees are like professors  Some are tall & thin  Short & boring a possibility  Others can be empty A BDC G H E F I J K

Trees vs. Binary Trees  Both represent parent-child relationships  Both consist of single "root" node & its descendants  Nodes can have at most one parent  Root nodes are orphans -- do not have a parent  All others, the non-root nodes must have parent  Children not required for any node in the tree  Nodes can have any number of children in tree  2 children for node in binary tree is the maximum

Binary Tree  Extends tree & adds following property  2 or fewer children per node  Child on left called “left child”  “Right child” name for other child node  For a level i in a binary tree  That level can have 2 i nodes  At most 2 (i+1) -1 nodes for tree to that level

Independent of Implementation A B Z F I Q M

For Next Lecture  Weekly assignment posted online  Due next Tuesday at 5PM  Ask me questions, if you have trouble on a problem  Textbook reading on traversals  How do we create a book’s table of contents?  Could we compute the space used by a directory?  How would we print out an arithmetic expression?